{
  "id": 3562,
  "curve_key": "97805752213619902403816384251641381605025:-30026996924037085815208058673419684022586757071643445062852625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-2037619837783747966746174671909195450105",
    "34753468662079960434777991387015015721532327315712767685272"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    4
  ],
  "naive_height": 283.1514060545074,
  "faltings_height": 21.488089262081505,
  "conductor": "519230428950677293578730527990684406193342087025",
  "bad_primes": [
    "3",
    "5",
    "7",
    "13",
    "19",
    "31",
    "37",
    "43",
    "47",
    "53",
    "79",
    "109",
    "113",
    "137",
    "167",
    "179",
    "263",
    "337",
    "823",
    "1171",
    "1471",
    "3461",
    "6269"
  ],
  "discriminant": "19667751412515156515533055946132194417701863641621100090781307553246650636386074058157193252660629043311153784267890625",
  "regulator": "11346322096910.320355328543245082321549997822433481898433919501",
  "points": [
    [
      "11949639957780658865",
      "110049901695902506986408261411"
    ],
    [
      "29075015544461710109",
      "9401830844632903409389699545"
    ],
    [
      "30111367139098642734",
      "26452949367690453270779744795"
    ],
    [
      "145348801310425612811/4",
      "745822356328947562351652720385/8"
    ],
    [
      "-93052184760977170903950482116/1797844801",
      "3015490901205682777833779135016155778148620/76230417407201"
    ],
    [
      "-26208948381729277084714765441/518290756",
      "1086764415027601302895479704040484953324705/11799407351096"
    ],
    [
      "1185225132894867484361/25",
      "26430650062203595872125308862919/125"
    ],
    [
      "30085495366678035420026/625",
      "3430717478704657738976727636700026/15625"
    ],
    [
      "87435943082503718761064/25",
      "25852288811258803800305995373070027/125"
    ],
    [
      "396061730037875457898301/27889",
      "433934768444192878749620629382768835/4657463"
    ],
    [
      "29132943835075310915891459/1267876",
      "11533846522781835974627743155924802995/1427628376"
    ],
    [
      "103007236122716761930896744/326041",
      "1035301890967456455733027726836944445045/186169411"
    ]
  ],
  "submitter": "Matej Jurasić",
  "history": [],
  "commentary": "Fibre at t = 83497/251378 of the Z/4 fibration E1 of X163 from Elkies–Klagsbrun (arXiv:2003.00077, Sec. 9), who list this t among their rank-12 parameters. The 12 generators were computed with PARI ellrank (2-isogeny descent).",
  "created_at": "2026-09-28 14:41:34",
  "updated_at": "2026-09-28 14:41:34"
}